Moduli of Hermite-Einstein Vector Bundles.
Moduli of Polarized Kahler Manifolds.
Moduli space, heights and isospectral sets of metrics
Moduli spaces of anti-self-dual connections on ALE gravitational instantons.
Moduli Spaces of Simple Bundles and Hermitian-Einstein Connections.
Moisezon Spaces and Almost Positive Coherent Sheaves.
Moments and Huygens' principle for conformally invariant field equations in curved space-times
Monge-Ampère equations and surfaces with negative Gaussian curvature
In [24], we studied the singularities of solutions of Monge-Ampère equations of hyperbolic type. Then we saw that the singularities of solutions do not coincide with the singularities of solution surfaces. In this note we first study the singularities of solution surfaces. Next, as the applications, we consider the singularities of surfaces with negative Gaussian curvature. Our problems are as follows: 1) What kinds of singularities may appear?, and 2) How can we extend the surfaces beyond the singularities?...
Monge-Ampère Equations, Geodesics and Geometric Invariant Theory
Existence and uniqueness theorems for weak solutions of a complex Monge-Ampère equation are established, extending the Bedford-Taylor pluripotential theory. As a consequence, using the Tian-Yau-Zelditch theorem, it is shown that geodesics in the space of Kähler potentials can be approximated by geodesics in the spaces of Bergman metrics. Motivation from Donaldson’s program on constant scalar curvature metrics and Yau’s strategy of approximating Kähler metrics by Bergman metrics is also discussed....
Monodromy and Picard-Fuchs equations for families of -surfaces and elliptic curves
Monogenic functions in conformal geometry.
Monogenic functions on surfaces.
Monopole metrics and the orbifold Yamabe problem
We consider the self-dual conformal classes on discovered by LeBrun. These depend upon a choice of points in hyperbolic -space, called monopole points. We investigate the limiting behavior of various constant scalar curvature metrics in these conformal classes as the points approach each other, or as the points tend to the boundary of hyperbolic space. There is a close connection to the orbifold Yamabe problem, which we show is not always solvable (in contrast to the case of compact manifolds)....
Monopoles over 4-manifolds containing long necks. I.
Monotone functions on symmetric spaces.
Monotone point-to-set vector fields.
More morphisms between bundle gerbes.
More on convolution of Riemannian manifolds.
Morphismes surjectifs de fibrés vectoriels semi-positifs
Morse index and bifurcation of p-geodesics on semi Riemannian manifolds
Given a one-parameter family of semi Riemannian metrics on an n-dimensional manifold M, a family of time-dependent potentials and a family of trajectories connecting two points of the mechanical system defined by , we show that there are trajectories bifurcating from the trivial branch if the generalized Morse indices and are different. If the data are analytic we obtain estimates for the number of bifurcation points on the branch and, in particular, for the number of strictly conjugate...